TSTP Solution File: ITP390_1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:30:47 EDT 2024
% Result : Theorem 62.79s 8.65s
% Output : CNFRefutation 62.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 188 ( 21 equ)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 35 ( 16 ~; 12 |; 4 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 143 ( 143 fml; 0 var)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 24 ( 22 usr; 12 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 45 ( 0 sgn 27 !; 12 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
tff(f10,axiom,
! [X0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] :
( 'fun_app$k'('uu$',X0)
<=> ? [X1: 'A_ell2_a_ell2_cblinfun$',X2: 'B_ell2_b_ell2_cblinfun$',X3: 'C_ell2_c_ell2_cblinfun$'] : ( 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X1),X2)),X3) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom9) ).
tff(f100,conjecture,
'fun_app$s'('f$','x$') = 'fun_app$s'('g$','x$'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture99) ).
tff(f101,negated_conjecture,
( ~ 'fun_app$s'('f$','x$') = 'fun_app$s'('g$','x$') ),
inference(negated_conjecture,[],[f100]) ).
tff(f102,axiom,
'member$a'('x$','collect$'('uu$')),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis100) ).
tff(f103,axiom,
! [X0: 'A_ell2_a_ell2_cblinfun$',X1: 'B_ell2_b_ell2_cblinfun$',X2: 'C_ell2_c_ell2_cblinfun$'] : ( 'fun_app$s'('f$','fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X0),X1)),X2)) = 'fun_app$s'('g$','fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X0),X1)),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom101) ).
tff(f262,axiom,
! [X0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$',X1: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$'] :
( 'member$a'(X0,'collect$'(X1))
<=> 'fun_app$k'(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom260) ).
tff(f857,plain,
'fun_app$s'('f$','x$') != 'fun_app$s'('g$','x$'),
inference(flattening,[],[f101]) ).
tff(f1544,plain,
! [X0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] :
( ( 'fun_app$k'('uu$',X0)
| ! [X1: 'A_ell2_a_ell2_cblinfun$',X2: 'B_ell2_b_ell2_cblinfun$',X3: 'C_ell2_c_ell2_cblinfun$'] : ( 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X1),X2)),X3) != X0 ) )
& ( ? [X1: 'A_ell2_a_ell2_cblinfun$',X2: 'B_ell2_b_ell2_cblinfun$',X3: 'C_ell2_c_ell2_cblinfun$'] : ( 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X1),X2)),X3) = X0 )
| ~ 'fun_app$k'('uu$',X0) ) ),
inference(nnf_transformation,[],[f10]) ).
tff(f1545,plain,
! [X0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] :
( ( 'fun_app$k'('uu$',X0)
| ! [X1: 'A_ell2_a_ell2_cblinfun$',X2: 'B_ell2_b_ell2_cblinfun$',X3: 'C_ell2_c_ell2_cblinfun$'] : ( 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X1),X2)),X3) != X0 ) )
& ( ? [X4: 'A_ell2_a_ell2_cblinfun$',X5: 'B_ell2_b_ell2_cblinfun$',X6: 'C_ell2_c_ell2_cblinfun$'] : ( 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X4),X5)),X6) = X0 )
| ~ 'fun_app$k'('uu$',X0) ) ),
inference(rectify,[],[f1544]) ).
tff(f1546,plain,
! [X0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] :
( ? [X4: 'A_ell2_a_ell2_cblinfun$',X5: 'B_ell2_b_ell2_cblinfun$',X6: 'C_ell2_c_ell2_cblinfun$'] : ( 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X4),X5)),X6) = X0 )
=> ( 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',sK17(X0)),sK18(X0))),sK19(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f1547,plain,
! [X0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] :
( ( 'fun_app$k'('uu$',X0)
| ! [X1: 'A_ell2_a_ell2_cblinfun$',X2: 'B_ell2_b_ell2_cblinfun$',X3: 'C_ell2_c_ell2_cblinfun$'] : ( 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X1),X2)),X3) != X0 ) )
& ( ( 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',sK17(X0)),sK18(X0))),sK19(X0)) = X0 )
| ~ 'fun_app$k'('uu$',X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19])],[f1545,f1546]) ).
tff(f1697,plain,
! [X0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$',X1: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$'] :
( ( 'member$a'(X0,'collect$'(X1))
| ~ 'fun_app$k'(X1,X0) )
& ( 'fun_app$k'(X1,X0)
| ~ 'member$a'(X0,'collect$'(X1)) ) ),
inference(nnf_transformation,[],[f262]) ).
tff(f2190,plain,
! [X0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$'] :
( ( 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',sK17(X0)),sK18(X0))),sK19(X0)) = X0 )
| ~ 'fun_app$k'('uu$',X0) ),
inference(cnf_transformation,[],[f1547]) ).
tff(f2361,plain,
'fun_app$s'('f$','x$') != 'fun_app$s'('g$','x$'),
inference(cnf_transformation,[],[f857]) ).
tff(f2362,plain,
'member$a'('x$','collect$'('uu$')),
inference(cnf_transformation,[],[f102]) ).
tff(f2363,plain,
! [X2: 'C_ell2_c_ell2_cblinfun$',X0: 'A_ell2_a_ell2_cblinfun$',X1: 'B_ell2_b_ell2_cblinfun$'] : ( 'fun_app$s'('f$','fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X0),X1)),X2)) = 'fun_app$s'('g$','fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X0),X1)),X2)) ),
inference(cnf_transformation,[],[f103]) ).
tff(f2474,plain,
! [X0: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun$',X1: 'A_b_prod_c_prod_ell2_a_b_prod_c_prod_ell2_cblinfun_bool_fun$'] :
( 'fun_app$k'(X1,X0)
| ~ 'member$a'(X0,'collect$'(X1)) ),
inference(cnf_transformation,[],[f1697]) ).
cnf(c_76,plain,
( ~ 'fun_app$k'('uu$',X0_51)
| 'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',sK17(X0_51)),sK18(X0_51))),sK19(X0_51)) = X0_51 ),
inference(cnf_transformation,[],[f2190]) ).
cnf(c_246,negated_conjecture,
'fun_app$s'('g$','x$') != 'fun_app$s'('f$','x$'),
inference(cnf_transformation,[],[f2361]) ).
cnf(c_247,negated_conjecture,
'member$a'('x$','collect$'('uu$')),
inference(cnf_transformation,[],[f2362]) ).
cnf(c_248,negated_conjecture,
'fun_app$s'('g$','fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X0_15),X0_27)),X0_52)) = 'fun_app$s'('f$','fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',X0_15),X0_27)),X0_52)),
inference(cnf_transformation,[],[f2363]) ).
cnf(c_355,plain,
( ~ 'member$a'(X0_51,'collect$'(X0_113))
| 'fun_app$k'(X0_113,X0_51) ),
inference(cnf_transformation,[],[f2474]) ).
cnf(c_43448,plain,
'fun_app$k'('uu$','x$'),
inference(superposition,[status(thm)],[c_247,c_355]) ).
cnf(c_45174,plain,
'fun_app$c'('fun_app$d'('tensor_op$a','fun_app$h'('fun_app$i'('tensor_op$c',sK17('x$')),sK18('x$'))),sK19('x$')) = 'x$',
inference(superposition,[status(thm)],[c_43448,c_76]) ).
cnf(c_49373,plain,
'fun_app$s'('g$','x$') = 'fun_app$s'('f$','x$'),
inference(superposition,[status(thm)],[c_45174,c_248]) ).
cnf(c_60682,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_49373,c_246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.06/0.12 % Command : run_iprover %s %d THM
% 0.11/0.32 % Computer : n031.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu May 2 22:28:16 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.17/0.44 Running TFA theorem proving
% 0.17/0.44 Running: /export/starexec/sandbox/solver/bin/run_problem --no_cores 8 --schedule casc_29_tfa --heuristic_context casc_unsat /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 62.79/8.65 % SZS status Started for theBenchmark.p
% 62.79/8.65 % SZS status Theorem for theBenchmark.p
% 62.79/8.65
% 62.79/8.65 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 62.79/8.65
% 62.79/8.65 ------ iProver source info
% 62.79/8.65
% 62.79/8.65 git: date: 2024-05-02 19:28:25 +0000
% 62.79/8.65 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 62.79/8.65 git: non_committed_changes: false
% 62.79/8.65
% 62.79/8.65 ------ Parsing...
% 62.79/8.65 ------ Clausification by vclausify_rel & Parsing by iProver...
% 62.79/8.65
% 62.79/8.65 ------ Preprocessing... sf_s rm: 146 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sf_s rm: 83 0s sf_e pe_s pe_e
% 62.79/8.65
% 62.79/8.65 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 62.79/8.65
% 62.79/8.65 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 62.79/8.65 ------ Proving...
% 62.79/8.65 ------ Problem Properties
% 62.79/8.65
% 62.79/8.65
% 62.79/8.65 clauses 731
% 62.79/8.65 conjectures 175
% 62.79/8.65 EPR 58
% 62.79/8.65 Horn 529
% 62.79/8.65 unary 131
% 62.79/8.65 binary 280
% 62.79/8.65 lits 1821
% 62.79/8.65 lits eq 268
% 62.79/8.65 fd_pure 1
% 62.79/8.65 fd_pseudo 0
% 62.79/8.65 fd_cond 18
% 62.79/8.65 fd_pseudo_cond 28
% 62.79/8.65 AC symbols 1
% 62.79/8.65
% 62.79/8.65 ------ Input Options Time Limit: Unbounded
% 62.79/8.65
% 62.79/8.65
% 62.79/8.65 ------
% 62.79/8.65 Current options:
% 62.79/8.65 ------
% 62.79/8.65
% 62.79/8.65
% 62.79/8.65
% 62.79/8.65
% 62.79/8.65 ------ Proving...
% 62.79/8.65
% 62.79/8.65
% 62.79/8.65 % SZS status Theorem for theBenchmark.p
% 62.79/8.65
% 62.79/8.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 62.79/8.65
% 62.79/8.65
%------------------------------------------------------------------------------